White Sox first baseman Jose Abreu may be drawing much of the attention during the first month of his major league career, but the Sox again demonstrated Monday night that their offense is more than just a one-man show.

On the day Abreu was named American League co-player of the week along with Mariners third baseman Kyle Seager, his Sox teammates fueled the offensive outbursts in a 7-3 victory over the Rays at U.S. Cellular Field.

Alejandro De Aza hit a two-run homer and Adam Eaton hit a two-run double to push the Sox a game above .500 at 14-13. They won three of four games for their first series victory over the Rays since 2012.

"A lot of guys feel like they're going to do something when they get up there," Sox manager Robin Ventura said. "That's not necessarily how it was last year. It's a good start, to get out of the gate like this offensively, to put that behind you. There's a feeling you're going to knock guys in. That's a contagious feeling when a team gets that."

Abreu, 27, added an RBI single in the eighth inning, his 32nd RBI this season. He has set MLB rookie records for the most home runs and RBIs in March/April.

"I was just like, 'Man, I know that's an award every player would like to have,'" Abreu said of the player of the week honor. "(The records) are one of those things you can't say, 'OK, I'm going to be able to do that.' The only thing I can do is I can thank God for allowing me to do that."

In his second start of the season, Sox right-hander Andre Rienzo lasted six innings, allowing three runs — two earned — on five hits, walking three and striking out four.

Rienzo, who is filling in for injured right-hander Felipe Paulino, gave up two first-inning runs and David DeJesus' RBI double in the fourth inning. Zach Putnam added two scoreless innings of relief.

"I don't know how long I'll be here, but I enjoy every day," Rienzo said. "Every day I live the dream."

Alexei Ramirez hit an RBI triple and Marcus Semien added a two-out RBI double to give the Sox a 4-3 lead in the bottom of the fourth off Rays right-hander Jake Odorizzi. He lasted just 41/3 innings, allowing eight hits and four runs, walking two and striking out five.

Eaton added a two-run double in the sixth inning off Rays reliever Jake McGee.